Is there enough room for five luggage?
The Guru Take
Request a large enough car
The amount of luggage you are allowed to bring with you is competely up to how much space is left in the vehicle you request. If you are referring to five large suitcases and you have multiple people in your family, I would imagine a regular sedan (that comes with UberBlack, UberX, Lyft, etc.) would be too small.
An SUV option that would send you a Suburban or Highlander do have a large cargo space in the back. So assuming the number of passengers does not exceed 3 or 4, you should have enough space in the back for five suitcases.